Electronic supplementary material Appendix Correlation coefficients between floral densities of predictors for bumble bee




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Electronic supplementary material
Appendix 1. Correlation coefficients between floral densities of predictors for bumble bee (Table S1A) and fly-visitation models (Table S1B)

Table S1A .Pearson correlation coefficients between floral densities of mainly bumble bee visited plant species.

 

Campanula rotundifolia

Centaurea jacea

Clinopodium vulgare

Euphrasia stricta

Hypericum maculatum

Knautia arvensis

Lotus corniculatus

Polygala vulgaris

Prunella vulgaris

Trifolium pratense

Trifolium repens

Campanula rotundifolia


































Centaurea jacea

-0.20































Clinopodium vulgare

0.14

0.23




























Euphrasia stricta

-0.20

0.28

0.24

























Hypericum maculatum

-0.14

0.07

0.08

0.10






















Knautia arvensis

0.15

0.07

-0.27

-0.22

-0.10



















Lotus corniculatus

-0.25

-0.15

-0.14

-0.22

-0.20

-0.08
















Polygala vulgaris

-0.40

-0.28

-0.33

-0.34

-0.13

-0.17

0.37













Prunella vulgaris

0.09

-0.25

-0.03

-0.25

-0.23

-0.17

0.17

-0.05










Trifolium pratense

0.14

-0.22

-0.10

0.09

0.24

0.08

-0.09

-0.10

0.18







Trifolium repens

0.02

-0.12

-0.22

-0.26

-0.25

0.24

-0.12

-0.05

-0.06

0.04




Note: High correlation coefficients will increase the possibility for multicollinearity among predictors and potentially affect the final model in stepwise regression analysis.




Table S1B. Pearson correlation coefficients between floral densities of mainly fly visited plant species

 

Galium album

Galium boreale 

Galium uliginosum

Galium verum

Leucanthemum vulgare

Plantago lanceolata

Potentilla erecta

Galium album






















Galium boreale 

-010



















Galium uliginosum

-012

031
















Galium verum

023

021

007













Leucanthemum vulgare

034

-015

003

016










Plantago lanceolata

-027

-020

-017

-036

-032







Potentilla erecta

012

-001

-009

001

010

020




Ranunculus acris

-024

-014

-016

-033

004

018

-006

Note: High correlation coefficients will increase the possibility for multicollinearity among predictors and potentially affect the final model in stepwise regression analysis



Appendix 2. Range of floral densities of predictors


Table S2. Floral densities (number of visual displays per plot, i.e. 2.25 m2) and mean visitation rates (visits per plot per 10 min) for predictor and response species

 

Mean floral density

Range of floral densities

Mean visitation

rate


Campanula rotundifolia

3.9

1-34

0.22

Centaurea jacea

0.5

1-6

1.37

Clinopodium vulgare

4.8

1-55

0.17

Euphrasia stricta

31.9

1-274

0.04

Hypericum maculatum

4.8

1-73

0.33

Knautia arvensis

0.2

1-3

1.59

Lotus corniculatus

3.9

1-105

0.07

Polygala vulgaris

6.4

1-93

0.04

Prunella vulgaris

4.1

1-53

0.35

Trifolium pratense

17.1

1-162

0.24

Trifolium repens

2.8

1-43

0.11

Galium album

8.9

1-144

0.01

Galium boreale 

5.8

1-92

0.02

Galium uliginosum

20.9

1-360

0.01

Galium verum

20.2

1-178

0.02

Leucanthemum vulgare

0.6

1-6

0.14

Plantago lanceolata

12.9

1-90

0.02

Potentilla erecta

41.0

1-290

0.08

Ranunculus acris

1.3

1-15

0.11



Appendix 3. Three sets of randomization models for bumble bee (Table S2A) and fly-visitation models (Table S2B)

We randomized the response variable 1000 times and for each permutation we made a new model employing the same procedures as for the original model used in the paper. Three sets of randomizations were performed: 1) Full randomization with no restriction (NULL), 2) randomization only between observations within the same plot accounting for spatial autocorrelation (PLOTS), and 3) randomization only between observations within the same day accounting for temporal autocorrelation (DAYS). The values presented are the mean number of predictor variables included in the final models (Total) as well as the mean number of predictor variables with a positive (+) or negative (-) relationship in the final model. The values are compared with the number of observed predictors in the regression models employed in the paper (OBSERVED). In general, randomizations resulted in fewer predictors than observed for models of bumble bee-visitation (Table S2A), whereas they showed slightly more predictors than observed in fly-visitation models (Table S2B). In particular, more positive (+) relationships were observed compared to the expected in models for bumble bee visitation.

Specifications: In a multiple regression around 5% of the predictor variables tested is theoretically expected to be statistically significant when the critical p-value is set to 0.05. Employing 9-11 predictor variables in the bumble bee-models, the mean number of predictors theoretically expected to be significant is ca. 0.45-0.55. For the NULL models of bumble bee visitation only two species (Knautia arvensis and Trifolium repens) have a considerably higher number of variables included in the randomized models than the theoretically expected (Table S2A). Only in the model of one species (T. repens) did the randomization resulted in a higher number of predictors in the final model than what was actually observed. For the PLOTS-models of bumble bee visitation a similar result was obtained, and one of the two species with expected number of significant predictors > 1 (Clinopodium vulgare and Trifolium pratense) had less than one predictor in the observed models. The models for other species had more observed predictors than expected. In the DAYS models the number of expected predictor variables in the final models increased considerably indicating a potential effect of temporal autocorrelation (but see below).

Using eight predictors in the fly-models leave us with a theoretical expectation of ca. 0.4 predictors included in the models, which is slightly lower than in most randomized models (Table 2SB). In most observed models for flies we do not find any significant predictors, except for visitation to Galium verum where the observed number of predictors are consistently higher than in the NULL, PLOT and DAY models.



A potential reason for the higher number of predictors in DAYS-models is that for most species the number of observations within the same day is restricted resulting in a limited number of combinations for the randomizations, hence the results of the simulation will approach the observed models. The clearest example of this is when the visitation rate of Leucanthemum vulgare is used as response variable (Table S2B). The restricted possibilities of combinations within the same day resulted in all randomizations leaving no predictor variable significant, which also is found in the observed model. Nevertheless, in DAYS- models for bumble bee-visitation only three of nine species (Centaurea jacea, C. vulgare and T. pratense) had more predictors expected than observed, and one species (Trifolium repens) had almost the same number of predictors as observed. In these cases where significant results were observed, but spatial or temporal autocorrelation could be suspected on basis of the simulation, we performed autocorrelation tests by means of the Mantel-test. This test was used to test the correlation between a matrix containing information about the numerical difference between the distance of plots (spatial autocorrelation; see also Hegland and Boeke 2006) or the numerical difference between sampling days (temporal autocorrelation) and a matrix containing the numerical difference in visitation rate among those same days for the response species in question. We used the Mantel Nonparametric Test Calculator 2.0 to perform these autocorrelation tests (available from Adam Liedloff’s webpage: http://www.terc.csiro.au/profile.asp?ID=LIEDA). The results showed that in the one species (T. pratense) where spatial autocorrelation could be suspected, there was no indications of autocorrelation in visitation rates among sampling plots (g= -0.52, r=-0.04). For those five specific response species (see above) where temporal autocorrelation could be suspected, only T. pratense (g=-1.9, r= 0.15) and Ranunculus acris (g=2.66, r=0.16) showed significant autocorrelation among sampling days, and both these had one (marginal) significant negative predictor in the final model (Table S3A and B). The other three species, which all had positive interactions with the floral densities of other species, all showed non-significant temporal autocorrelation (C. jacea: g=1.23, r= 0.09; C. vulgare: g=0.51, r=-0.03; and T. repens: g=-1.40, r= -0.09). Based on these tests we can conclude that most results are not inflated by autocorrelation, but that the two negative relationships observed for T. pratense and R. acris should be interpreted with care.


Table S3A. Three sets of randomization models for bumble bee visitation-models compared to observed models. Numbers are mean number of variables expected by chance based on 1000 permutations.

Flower visitation rate

NULL

PLOTS

DAYS

OBSERVED

-

+

Total

-

+

Total

-

+

Total

-

+

Total

Campanula rotundifolia

0.34

0.30

0.64

0.25

0.23

0.48

0.47

1.21

1.69

1

2

3

Centaurea jacea

0.36

0.35

0.70

0.33

0.42

0.75

0.13

0.94

1.08

0

1

1

Clinopodium vulgare

0.33

0.39

0.71

0.39

0.71

1.11

0.24

1.18

1.42

0

4

4

Euphrasia stricta

0.29

0.43

0.72

0.52

0.31

0.82

0.40

0.37

0.77

0

2

2

Hypericum maculatum

0.27

0.28

0.56

0.38

0.31

0.70

0.24

0.52

0.76

1

0

1

Knautia arvensis

0.54

0.49

1.02

0.44

0.39

0.83

1.74

1.13

2.86

2

2

4

Prunella vulgaris

0.34

0.34

0.68

0.34

0.13

0.47

0.09

0.89

0.98

0

2

2

Trifolium pratense

0.24

0.33

0.57

0.61

0.56

1.17

1.20

0.19

1.40

1

0

1

Trifolium repens

0.52

0.52

1.04

0.49

0.15

0.63

0.36

0.63

0.99

0

1

1




Table S3B. Three sets of randomization models for fly visitation-models compared to observed models. Numbers are mean number of variables expected by chance based on 1000 permutations.

Flower visitation rate

NULL

PLOTS

DAYS

OBSERVED

-

+

Total

-

+

Total

-

+

Total

-

+

Total

Galium uliginosum

0.48

0.60

1.08

0.29

1.37

1.65

0.06

0.04

0.10

0

0

0

Galium verum

0.26

0.30

0.56

0.05

0.07

0.12

0.01

1.73

1.74

0

3

3

Leucanthemum vulgare

0.34

0.32

0.65

0.13

0.62

0.75

0.00

0.00

0.00

0

0

0

Plantago lanceolata

0.35

0.43

0.77

0.33

1.26

1.58

0.25

0.05

0.30

0

0

0

Potentilla erecta

0.23

0.21

0.44

0.12

0.07

0.18

0.37

0.15

0.52

0

0

0

Ranunculus acris

0.39

0.35

0.73

0.38

0.37

0.76

0.92

0.16

1.08

1

0

1


Appendix 4. Species list: the 11 Bombus species and 30 most common Diptera species observed in Rudsviki, Kaupanger, Norway in 2003 and 2004.

Bombus ssp. includes both social bumble bees and cuckoo bumble bees (former Psithyurs sp.). Species are presented in alphabetic order.



Bombus:

Bombus campestris

Bombus flavidus

Bombus hortorum

Bombus jonellus

Bombus lapidarius

Bombus lucorum

Bombus monticola

Bombus norvegicus

Bombus pascuorum

Bombus pratorum

Bombus sylvestris

Diptera:

Bellardia vulgaris

Cheilosia longula

Cheilosia scutellata

Cheilosia vicina

Chrysotoxum arcuatum

Dasysyrphus pinastri

Dasysyrphus venustus

Empis pennipes

Empis syrovatkai

Eriothrix rufomaculatus

Eupeodes nitens

Helina quadrum

Hydrophoria lancifer

Melanomya nana

Meliscaeva cinctella

Parasyrphus vittiger

Phaonia angelicae

Phasia aurulans

Platymya fimbriata

Rhamphomyia nigripennis

Sarcophaga variegata

Sphaerophoria scripta

Sphaerophoria taeniata

Syrphus ribesii

Syrphus torvus

Thricops cunctans

Thricops innocuus

Thricops nigrifons

Thricops semicinereus

Volucella pellucens


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